Question 207711: Solve for X, Y, and Z in the following systems of three equations using either substition or elimination methods: a. X + 2Y + Z = 6 X + Y = 4 3X + Y + Z = 8 b. 10X + Y + Z = 12 8X + 2Y +Z = 11 20X - 10Y - 2Z = 8 c. 22X + 5Y + 7Z = 12 10X + 3Y + 2Z = 5. Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.

Calculator Use

Enter 2 sets of coordinates in the 3 dimensional Cartesian coordinate system, (X₁, Y₁, Z₁) and (X₂, Y₂, Z₂), to get the distance formula calculation for the 2 points and calculate distance between the 2 points.

Accepts positive or negative integers and decimals.

X Y Z Solver

Distance Formula:

The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 3 dimensional plane, the distance between points (X₁, Y₁, Z₁) and (X₂, Y₂, Z₂) is given by:

[ d = sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 + (z_{2} - z_{1})^2} ]

How to Calculate Distance between 2 points

To calculate the distance between 2 points, (X₁, Y₁, Z₁) and (X₂, Y₂, Z₂), for example, (5,6,2) and (-7,11,-13), we plug our values into the distance formula:

[ d = sqrt {(-7 - 5)^2 + (11 - 6)^2 + (-13 - 2)^2} ]

combining terms inside parentheses we get:

[ d = sqrt {(-12)^2 + (5)^2 + (-15)^2} ]

squaring terms we get,

[ d = sqrt {144 + 25 + 225} ]

adding the 3 results,

[ d = sqrt {394} ]

finally,

[ d = 19.849433 ]

Cite this content, page or calculator as:

Furey, Edward '3D Distance Calculator'; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Solve System of Linear Equations

This section shows you how to solve a system of linear equationsusing the Symbolic Math Toolbox™.

Solve System of Linear Equations Using linsolve

A system of linear equations

$$\begin{array}{l}{a}_{11}{x}_1+a_{12}{x}_2+\dots +a_{1n}{x}_n=b_1\\ a_{21}{x}_1+a_{22}{x}_2+\dots +a_{2n}{x}_n=b_2\\ \cdots \\ a_{m1}{x}_1+a_{m2}{x}_2+\dots +a_{mn}{x}_n=b_m\end{array}$$

can be represented as the matrix equation $$A\cdot \overrightarrow{x}=\overrightarrow{b}$$, where A isthe coefficient matrix,

and $$\overrightarrow{b}$$ is the vector containing theright sides of equations,

If you do not have the system of linear equations in the form AX= B, use equationsToMatrix to convertthe equations into this form. Consider the following system.

Declare the system of equations.

Use equationsToMatrix to convert the equationsinto the form AX = B. The second input to equationsToMatrix specifiesthe independent variables in the equations.

Use linsolve to solve AX = B forthe vector of unknowns X.

X Y And Z Solver Equations

From X, x = 3, y = 1 and z = -5.

Solve System of Linear Equations Using solve

Use solve instead of linsolve ifyou have the equations in the form of expressions and not a matrixof coefficients. Consider the same system of linear equations.

Solving X Y Z Equations

Declare the system of equations.

Solve the system of equations using solve.The inputs to solve are a vector of equations,and a vector of variables to solve the equations for.

solve returns the solutions in a structurearray. To access the solutions, index into the array.

X+y=z Solve

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